EuclideanGeometry.Sphere.IsDiameter.sbtw
∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {s : EuclideanGeometry.Sphere P} {p₁ p₂ : P},
s.IsDiameter p₁ p₂ → s.radius ≠ 0 → Sbtw ℝ p₁ s.center p₂- Defined in
- Mathlib.Geometry.Euclidean.Sphere.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- EuclideanGeometry.Spherestatement and proof · cited by 233
- EuclideanGeometry.Sphere.centerstatement · cited by 181
- EuclideanGeometry.Sphere.radiusstatement and proof · cited by 123
- Sbtwstatement and proof · cited by 122
- EuclideanGeometry.Sphere.IsDiameterstatement and proof · cited by 31
- EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_centerproof · cited by 11
- sbtw_midpoint_of_neproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.angle_center_eq_pi_iff_isDiameterproof · cited by 0